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Vol  II.  No.  2. 


reprinted  from 

March,  1895. 

THE 


Psychological    Review 


J.  MARK   BALDWIN 
Princeton  University 


EDITED  £  y 

J.   McKEEN  CA'ITELI. 
^^"  Columbia  College 

with  the  co-operation  of 

ALFRED   BINET,    £colk  des  Hautes-Studes,  Paris;    JOHN  DEWEY,  University  of 

Chicago;   H.  H.  DONALDSON,  University  ok  Chicago;   G.  S.  FULLERTON, 

Universitv  OF  Pennsylvania;    WILLIAM  JAMES,  Harvard  University  ; 

JOSEPH  JASTROW,  University  of  Wisconsin  ;   G.  T.  LADD,  Yale 

University;   HUGO  MUNSTERBEKG,  Harvard  University; 

M.  ALLEN  STARR,  College  of  Physicians  and  Surgeons, 

New  York;  CARL  STUMPF,  University,  Berlin; 

and  JAMES  SULLY,  University  College, 

London. 


CONTENTS. 


105 


130 


149 


^73 


The  Knozving  of  Things  Together:   William  James 

Contributions  from  the  Psychological  Laboratory  of  Columbia  Col- 
lege {III.)  Experiments  mi  Dermal  Sensations :  Harold 
Griffing.      The  After-image   Threshold:   S.  I.   Franz 

Normal  Defect  of  V  tsion  m  the  tovea  :    Christine  Ladd  Franklin 

Proceedings  of  the  Third  Annual  Meeting  of  the  American  Psycho- 
logical Association,  Princeton,  i8g^       ..... 

Discussio7i  :  The  Sensatiora  are  not  t lie  Emotion :  Ci.  M.  Stratton.  A 
Correction  .•  W.  J.       . 

Psychological  Literature :  .         .         .         .         .  .  175 

Philosophical  Remains  of  George  Croom  Robertson  :  J.  S.,  175.  Wundt's 
Lectures  on  Human  and  Animal  Psychology :  A.  Kirschmann,  179. 
Ladd' s  Primer  of  Psychology :  G.  S.  F. ,  180.  Deussens  Elements  of 
Metaphysics :  A.  T.  Ormond,  181,  Lfyslop's  Elements  of  Ethics:  A.  T. 
Ormond,  184.  Johnson's  U?nver sal  Cyclopedia,  L-V.:  J.  D.  Evolution 
a?id  Biology  [Osborn's  From  the  Greeks  to  Dar^vin,  IVillty's  Amphioxus, 
Jor don's  Factors  in  Organic  Evolution,  Gould's  Dictionary  of  Biology, 
Collins'  Epitome  of  the  Synthetic  Philosophy^:  J.  M.  B.,  189.  Child 
Psychology:  F.  Tracy,  190.  Neurology:  H.  H.  D.,  194.  Hearing: 
F.  Angell,  197.  Attention  and  Memory :  H.  N.  Gardiner,  199.  Re- 
action-Time: J.  McK.  C,  200.  Judgment  and  Belief :  G.  M,  Duncan, 
209.  Pathological  (^Ziehen's  Psychiatric,  Dumas'  Mt'latuJudie,  Charcofs 
Cliniques  des  maladies:  William  Noyes,  A.B.,  209.      Ne^v  Books,  214. 

Psychological  Questioning,  215.      Notes,  216. 


published  bi-monthly  bv 
MACMILLAN    AND    CO., 

66  FIFIH    AVENUE,   NEW   YORK;    AND    LONDON. 

Single  Numbers,  75  cents  (3s.)  Annual  Subscription,  $4.00  (168.  6d. 

Beilin,  Mayer  &  MUUer  (M.  16.50),  Paris,  H.  Welter  (Fr.  21), 

Markgrafen  Str.,  51.  Rue  Bonaparte,  59. 

Copyright,  1895,  by  MAcmuaN  k  Co. 

Entered  kt  the  Post-office  at  New  York  as  decond-claM  Matt«r. 


f 


3? 


^  CONTRIBUTIONS    FROM    THE    PSYCHOLOGICAL 

LABORATORY  OF  COLUiMBIA  COLLEGE.     (IIL) 


EXFEKIMKNTS    ON    DeKMAL    SENSATIONS.' 
IJV    HAROLD    GRIFFING. 

The    Relation    betiveen    the    fnteiisity  of  the   Sti)nuli(s  and    its 

Estimated  bitensity. 
\  ^ 

\Two  stimuli  differiiiij  greatly  in  intensity  were  success- 

iveiy  applied  to  the  hand  of  the  observer,  and  he  was  re- 
quired to  jud<^e  how  much  greater  one  was  than  the  other. 
The  pressure  was  given  by  weights  placed  in  the  pan  of  a 
balance,  and  was  transmitted  to  the  hand  by  a  wooden  rod 
attached  to  the  pan.  The  stimuli  were  2,  10,  50,  250,  1250, 
and  1800  grams.  The  area  of  stimulation  was  that  of  a  cir- 
cle 4  mm.  in  diameter.  The  experiments  made  on  four 
observers  showed  that  on  the  average  10  g.  was  considered 
about  twice  as  heavy  as  2  g.  ;  50  g.  twice  as  heavy  as  10  g. ; 
250  g.  three  times  as  heavy  as  50  g. ;  1250  g.  five  times  as 
heavy  as  250  g. ;  and  i8oog.  three  times  as  heavy  as  1250  g. 
It  thus  appears  that  for  low  and  moderate  intensities  the 
estimate  of  intensity  increases  much  more  slowly  than  the 
objective  intensity;  but  as  the  stimulus  approaches  the 
pain  threshold,  the  reverse  appears  to  be  the  case.  Indi- 
viduals differ,  however,  in  their  underestimation  of  low 
intensities,  and  also,  but  to  a  greater  degree,  in  tlicir  over- 
estimation  of  high  intensities. 

The  Discritnination  of  Weights  of  Different  Intensities. 

Cylindrical  boxes  filled  with  shot  served  as  stimuli.  The 
method  used  was  that  of  right  and  wrong  cases;  that  is,  the 
stimuli  were  placed  successively  upon  the  hand,  and  the  ob- 

^  A  full  account  and  discussion  of  these  experiments  will  be  found  in  the  writer's 
dissertation,  On  Sensations  from  Pressuri-  an<i  Impact.  Supplement  Monograph 
(No.  i)  to  this  Review. 


i^J'UO 


126  HAROLD  GRIFFING. 

server  was  asked  to  decide  which  was  heavier.  The  accu- 
rac}\of  discrimination  is  measured  by  the  probable  error,  or 
that  increment  which  the  observer  perceives  correctly  75% 
of  the  tlme.^  Thus  the  greater  the  probable  error  the  less 
the  accuracy  of  discrimination.  The  stimuli  varied  from 
100  to  3200\g..  no  more  than  four  intensities  being  used  for 
any  one  observer.  The  results  of  9040  experiments  made 
on  5  observers  showed  that  the  probable  error  for  pressure 
stimidi  tends  to  increase  in  proportion  to  the  intensity  of 
the  stimulus  within  the  approximate  limits  300-3000  g.  For 
low  intensities  the  probable  error  increases  much  more 
slowly  than  the  stimulus.  For  5-7  g.  the  probable  error 
for  a  good  observer  was  |-  of  the  stimulus.  For  high  inten- 
sities also  there  seems,  to  be  a  similar  tendency,  but  it  is  not 
so  marked.  As  illustrative  of  our  results,  we  give  the  prob- 
able errors  in  grams  for  McW.  :  for  100  g.,  19;  for  500  g., 
36;  for  1500  g.,  112;  for  3200  g.,  193.  The  average  value 
of  the  probable  error  for  all  stimuli  (100  g.  and  above)  and 
all  observers  was  approxirtiately  \  of  the  stimulus.  That 
is  we  can,  on  the  average,  judge  correctl}'  whether  one 
stimulus  is  heavier  or  lighter  than  another  75%  of  the  time 
when  the  stimuli  are  in  the  ratio  9:  10. 

In  these  experiments  the  constant  error,  or  tendency  to 
overestimate  the  second  stimulus,  was  found  to  be  for  some 
persons  very  great,  running  as  high  as  \  of  the  stimulus. 
The  constant  error  is  more  variable  than  the  probable  error; 
the  expression  'constant  error'  is  thus  quite  misleading. 
The  constant  error  seems  to  be  greater  for  observers  having 
a  large  probable  error.  A  great  constant  error  for  pressure 
is  not  necessarily  accompanied  by  a  similar  overestimation 
for  lifted  weights. 

The  degree  of  confidence  was  studied  by  having  the  ob- 
servers say  a,  b,  c  and  d,  according  as  they  were  certain, 
quite  confident,  less  confident,  or  doubtful.  Individuals 
differ  greatly  in  their  confidence,  the  percentage  of  wrong 
judgments  of  which  observers  were  confident  varying  from 
2%  to  33%.     The  probability  of  correctness  when   confident 

*  This  quantity  has  been  considered  to  be  equivalent  to  the  least  noticeable  differ- 
ence.    It  is  doubtful,  however,  if  such  a  relation  can  be  justified. 


EXPERIMENTS  ON  DERMAL  SENSATIONS.  12/ 

\, 
was  fo'i^  most  observers  about  .8  to  .9.      There  appears  to  be 
no  relation  between  these  quantities  and  the  accuracy  of  dis- 
criminatiQn.      The  percentage  of  correct  guesses  varied  from 
52%  Lo  /u^,  the  average  being  59%. 

The  Place  of'  Sthnulation. 

The  accuracy  of  discrimination  for  weights  of  100  g.  or 
more  is  not  for  two  observers  apprecial)ly  different  for  the 
pahii  of  the  handV,  the  back  of  the  hand,  and  the  vohir  sur- 
face of  the  third  phalanx  of  the  index  finger.  For  5-7  g.  it 
was  found  at  first  to  be  much  less  for  the  back  of  the  hand 
and  wrist  than  for  the  index  finger  of  one  observer,  but 
to  increase  greatly  by  practice.  Stimuli  of  low  intensity,  5 
and  100  g.,  when  placed  on  the  forearm,  tended  to  be  judged 
lighter  than  when  placed  on  the  finger.  This  result  was 
obtained  by  placing  a  weight  first  on  the  finger  and  then  on 
the  arm,  increments  being  added  until  the  weights  seemed 
equal. 

The  writer  tested  the  sensitiveness  to  pain  at  different 
parts  of  the  body  by  the  algometer.'  It  was  found  that  the 
sensitiveness  is  greatest  where  the  skin  is  thin  and  not  sepa- 
rated from  the  bone  by  other  tissues.  Among  the  most  sen- 
sitive parts  are  the  upper  regions  of  the  head,  whereas  the 
palm  of  the  hand,  the  thigh  and  the  heel  are  among  the  least 
sensitive  parts.  \ 

Sensations  from  Impact.  ""■ 

The  tactile  threshold  for  pressure  stimuli  without  move- 
ment was  found  by  observing  the  angular  elevation  of  a 
bristle  which  was  attached  at  one  end  to  a\wooden  handle, 
and  at  the  other  could  transmit  pressure  to  the  skin.  In 
this  way  it  was  found  that  .4  g.  is  about  as  easilv  perceived 
when  movement  is  thus  excluded,  as  is  .01  g..  when  the 
stimulus  is  placed  carefully  upon  the  hand.  The  difference 
in  the  results  is  due  to  the  sensory  effect  of  movement. 

By  dropping  weights  upon  the  hand,  the  heights  were 
found  at  which  different  weights  caused  pain.  The  weights 
were  25,  100,  200  and  300  g.      The   area  of   stimulation    was 

'  An  instrument  by  which  pressure  could  be  exerted  up  to  15  k. 


128  HAROLD  GRIFFING. 

\ 

constant,  a  circle  about  i  cm.   in  diameter.      The   results  of 

60  measurements  showed  that  the  product  of  the  mass  and 

hei.^ht    pain-thresholds   is   fairly   constant.      As   the    height 

through  \vhich  a  body  falls  is  proportional  to  the  square  of 

the  velocity,  the  pain  threshold  and  therefore  the  intensity 

of  pain,  depend  as  much  upon  the  square  of  the  velocity  as 

upon  the  mass  of  a  striking  object. 

By  the  method  of  right  and  wrong  cases  we  studied  the 
accuracy  of  discrimination  for  impact  stimuli.  The  results 
of  800  experiments  showed  that  a  weight  of  50  g.,  falling 
through  17.5  cm,,  is  judged  about  as  well  as  1000  g.  without 
movement.  The  average  probable  error  for  pressure  only 
was  y^Y  of  the  stimulus  for  S.  F.,  and  Jj  for  L.  F.  For  im- 
pact the  corresponding  values  were  -^-^  and  y!^. 

In  900  experiments,  carried  on  in  the  same  way,  the 
weight  was  kept  constant  and  the  observer  required  to  esti- 
mate differences  in  the  intensity  of  the  blow  due  to  differ- 
ences in  height  and  therefore  velocity.  The  results  were 
compared  with  those  based  upon  the  same  number  of  experi- 
ments on  the  same  observers,  in  which  the  height  was 
constant  and  the  weight  variable.  We  found  that,  on  the 
whole,  differences  in  weight  are  judged  less  accurately  than 
differences  in  velocity,  but  more  accurately  than  differences 
in  the  square  of  the  velocity..  But  great  individual  varia- 
tions occur. 

Experiments  were  also  made  on  the  intensive  effect  of 
the  weight  as  compared  to  that  of  the  velocity.  A  100  g. 
weight  having  fallen  upon  the  hand  from  a  height  of  5  cm., 
the  height  was  found  at  which  25  g.  would  cause  a  sensation 
of  the  same  intensity.  Here  also  observers  differed  greatly. 
The  average  height  for  5  observers  was  38  cm.,  the  maxi- 
mum being.  58,  the  minimum  20  cm.  Hence  the  mass  has  in 
general  greater  intensive  effect  than  the  height  or  the  square 
of  the  velocity.  Otherwise  the  average  height  found  would 
be  about  20  cm.  On  the  other  hand,  the  mass  has  less  effect 
than  the  velocity  or  square  root  of  the  height. 

The  Area  of  Stimulation. 

In  the  experiments  on  Weber's  law  two  areas  were  used, 
8  sq.  cm.  and  .12  sq.  cm.  approximately.      It  was  found  that 


EXPERIMENTS  ON  DERMAL  SENSATIONS.  1 29 

■on  the  whole  this  difference  of  area  did  not  affect  the  accu- 
racy of  discrinrination  for  weights.  Individual  variati(jns, 
however,  were  \yery  marked. 

If  stimuli  of  the  same  weight,  but  different  areas,  be 
placed  successively  upon  the  hand,  the  stimulus  applied  on 
the  smaller  area  will  be  overestimated.  By  applying  the 
method  of  right  and  wrong  cases  we  measured  this  overesti- 
mation.  The  results  of  400  experiments  on  one  observer 
gave  an  overestimation  of  \  of  the  stimulus  at  200  g.  Ex- 
periments by  a  different  application  of  the  method  of  right 
and  wrong  cases  on  5  observers  gave  about  the  same  result, 
except  that  one  observei^  showed  a  tendency  to  underesti- 
mate, rather  than  overestimate,  the  stimulus  applied  to  the 
smaller  area.  By  a  third  method,  however,  we  found  a 
decided  overestimation  for  Qnly  2  out  of  5  observers.  From 
these  experiments  on  10  observers,  we  conclude  that  this 
tendency  is  by  no  means  universal. 

The  effect  of  alterations  iii  the  intensity  of  pressure  on 
the  accuracy  of  discrimination  pf  areas  was  investigated  by 
the  method  of  right  and  wronff  cases,  differences  in  area 
being  judged  instead  of  differences  in  intensity.  The  stand- 
ard areas  used  were  i  and  8  sq;  cm.  and  the  intensities 
200  and  800  grams.  The  results  Ojf  1900  experiments  on  3 
observers  showed  that  the  accuracy  of  discrimination  for 
areas  was,  on  the  average,  about  \  greater  for  200  g.  than 
for  800  g. 

By  placing  thin  circular  cards  upon  the  hand  and  apply- 
ing pressure  upon  these,  we  studied  the  effect  of  variations 
in  the  area  on  the  so-called  tactile  threshold.  The  areas 
were  approximately  \  mm.,  10  mm.  and  90  mm.  The  aver- 
ages of  the  corresponding  threshold  values,  based  upon  60 
experiments,  were  for  F.,  .2  g.,  .9  g.  and  r.9  g.  ;  and  for  the 
writer,  .5  g.,  1.4  g.  and  1.6  g.  Thus  the  smaller  the  area 
the  greater  the  probability  that  stimuli  of  low  intensity  will 
be  perceived. 

In  a  similar  manner  the  relation  of  the,  pain  threshold 
to  the  area  of  stimulation  was  investigated.,  The  averagfe 
values  of  the  pain  threshold,  based  upon  80  experiments  on 
two  observers,  were:    for    10   mm.,   i.4kilog.  ;    for  30  mm.. 


1 30  SHEPHERD  IVOR  Y  FRANZ. 

2.8  kilog.  ;  for  90  mm.,  4.4  kilog.  ;  and  for  270  mm.,  6.6 
kilog.  Thus  the  pain  threshold  increases  with  the  area; 
but,  like  the  tactile  threshold,  much  more  slowl}-  than  in 
direct  proportion. 

The   Time  of  Stivuilation.  '' 

The  sensory  effect  of  pressure  stimuli  of  low  intensity 
was  found  to  depend  upon  the  rate  at  which  the  pressure 
was  increased.  The  instrument  used  was  that  referred  to  in 
the  experiments  already  described  on  the  tactile  threshold. 
By  this  pressure  was  exerted  upon  the  palm  of  the  observer's 
hand  up  to  .4  g.,  at  different  rates  of  increase.  These  rates 
were  approximately  .05  g.,  .3  g.  and  2  g.  per  second.  The 
corresponding  percentages  of  times  the  stimulus  was  per- 
ceived in  300  experiments  on  2  observers  were  6%,  32%,  and 
82%.  Thus  the  greater  the  rate  of  increase  the  greater  the 
probability  of  perception. 

The  time  in  which  dernial  stimuli  of  different  intensities 
cause  pain  was  found  in  the  following  manner.  Different 
weights  were  placed  in  a  balance  pan  so  as  to  press  upon 
the  palm  of  the  hand,  and  the  time  was  noted  which  elapsed 
before  the  appearance  of  pain.  The  pressure  was  commu- 
nicated from  the  pan  to  the  hand  by  a  wooden  rod  fastened 
to  the  pan.  The  diameter  of  the  base  was  1.5  mm.  The 
averages  in  seconds,  based  upon  80  experiments  on  2  ob- 
servers, are  as  follows:  for  100  g.,  230  sec.  ;  for  200  g.,  35 
sec.  ;  for  300  g.,  10  sec.  ;  for  500  g.,  4.5  sec.  It  is  evident, 
therefore,  that  the  time  as  well  as  the  area  and  intensity  of 
stimulation  determine  the  sensory  effect.  There  is,  how- 
ever, an  intensive  limit,  below  which  pressure  stimuli  never 
become  painful.  This  is  probablv  from  25  to  50  g.  for  the 
area  used. 


-*wo.-.-'y*'<t^'>''A'?"".' 


The  After-Image  Threshold. 

by  shepherd  ivory  fraxz. 

Ever   since  Aristotle  described   in   his  De  Somniis^    the 
appearance  of  an  after-image,  the  phenomena  have  attracted 

'  Thfs  seems  not  to  be  generally  known  by  German  writers.     Aubert  and  Helm- 
holtz  both  credit  Peiresc  as  being  the  first  to  mention  after-images. 


THE  AFTER-IMAGE    THRESHOLD. 


i3« 


attention.  St.  Augustine  mentions  them,  and  in  modern 
times  such  prominent  men  as  Buffon,  Goethe  and  Newton 
have  described  their  appearance.  But  very  little  was  ac- 
complished beyond  the  making  of  theories  until  this  century, 
when  Plateau,  Seguin,  Fechner  and  others  studied  the  color 
changes.  Up  to  the  present  time  practically  nothing  has 
been  accomplished  in  the  way  of  exact  measurement. 

The  present  paper  gives  the  results  of  an  attempt  to 
measure  the  smallest  amount  of  light  which  will  produce  an 
after-image.  For  this  purpose  three  physical  units  had  to  be 
considered — the  intensity  of  the  light,  its  area,  and  the  time  of 
stimulation.  The  apparatus  used  was  planned  and  formerly 
used  by  Prof.  Cattcli,  but  was  adapted  by  the  writer.  It  is 
represented  in  the  accompanying  cut. 

FiCLRE    1. 


S  is  an  upright  iron  screen  pierced  by  a  hole(H)  through 
which  the  ligiit  from  the  hooded  lamp  (L)  may  pass  to  the 
observer  on  the  other  side  of  the  screen.  P  is  a  seconds 
pendulum.  To  this  is  attached  a  piece  of  sheet  iron  which 
covers  the  hole  when  the  pendulum  is  held  up  by  the  electro- 
magnet (M).  The  key  (K)  which  makes  and  breaks  the  cur- 
rent to  the  magnet  (M)  is  managed  by  the  experimenter,  and 


132  SHEPHERD  IVORY  FRANZ. 

the  pendulum  is  held  up  or  let  swing  at  his  pleasure.  By 
breaking  and  making  the  current  the  pendulum  swings,  per- 
mits the  light  to  be  seen  by  the  observer  for  exactly  one 
second,  and  is  caught  up  again  by  the  magnet.  The  lamp  is 
moved  along  the  arm  (A),  increasing  or  decreasing  the 
intensity  of  the  light.  The  opening  (H)  was  covered  with 
ground  glass.  -^-^  candle  power  was  found  a  convenient 
intensity,  this  being  increased  by  moving  the  lamp  nearer 
the  observer,  and  decreased  by  moving  it  away  from  the 
observer.  The  lamp  was  used  at  the  distances  i,  i,  i,  2 
and  4  meters,  and  so  far  as  the  intensity  decreases  inversely 
as  the  square  of  the  distance,  the  respective  intensities  would 
be  2*5,  2V'  TW'  TTir  ^"*^  tgVtt  candle  power.  The  absorbing 
power  of  the  ground  glass  was  found  to  be  SC/^,  whence 
the  intensities  were  decreased  by  half — making  the  series — 
_2^,  ^1^,  -1-,  ^^^,  ^  1  --,  c.  p.  In  the  experiments  on  inten- 
sity, the  time  of  exposure  (one  second)  and  the  area  (64 
sq.  mm.)  were  kept  constant.  For  the  experiments  on  area, 
the  lamp  was  placed  at  a  distance  of  ]  m.,  thus  making  the 
intensity  -^-^  c.  p.,  the  time  (one  second)  being  the  other 
constant.  The  area  was  changed  by  using  different  pieces 
of  ground  glass  on  which  black  paper  blocked  off  all  but  the 
small  area  required.  The  areas  used  were  64,  16,  4,  i,  i,  ^-^ 
sq.  mm.  When  time  was  the  changeable  unit,  the  area  (64 
sq.  mm.)  and  the  intensity  {^^^  c.  p.)  were  the  constants.  The 
series  consisted  of  four  times,  -^-^^^  3-575-,  yV  ^^i^  ^  second. 
The  shorter  times  were  obtained  by  means  of  drop  screens, 
made  of  pasteboard  and  weighted.  As  they  did  not  fall  in 
grooves  there  was  no  appreciable  friction,  and  hence  the 
real  time  practically  corresponded  with  the  theoretical  time. 
The  screen  was  on  the  side  of  the  apparatus  near  the 
observer,  and  therefore  is  not  shown  in  the  cut.  The  time 
one  second  was  given  by  the  pendulum.  As  will  be  noticed, 
there  was  a  common  unit  in  the  three  series,  i.  e.,  when  the 
experiments  were  made  with  i  sec,  64  sq.  mm.  and  2V  c.  p. 
The  experiments  were  conducted  in  a  dark  room,  and  all 
observations  were  made  with  the  eyes  open,  so  as  not  to 
disturb  the  after-image.  A  cloth  curtain  was  hung  across 
the  room,  shutting  off  from  the  observer  everything  but  the 


riiE  after-image  threshold.  133 

small  opening  in  the  screen.  The  observer's  eyes  were  30 
cm.  from  the  openin<^,  his  head  being  steadied  by  a  support. 
Before  any  experiments  weie  made  a  rest  of  ten  minutes 
was  taken  to  allow  the  observer's  eyes  to  become  accustomed 
to  the  darkness;  between  the  disajjpearance  of  one  after- 
image and  the  next  stimidus  there  was  a  rest  of  thirtv 
seconds.  When  the  thirty  seconds  had  elapsed  a  signal  was 
given,  five  seconds  were  allowed  for  preparation,  and  the 
stimulus  was  produced. 

Very  few  difficulties  presented  themselves,  and  of  these 
the  only  one  not  overcome  was  the  lack  of  a  fixation  point, 
as  any  fixation  point  was  apt  to  produce  a  disturbing  after- 
image. By  practice,  however,  the  observer  learned  to  look 
in  a  certain  way  for  the  stimulus,  and  in  the  case  of  the 
writer  not  over  five  per  cent,  of  the  time  were  the  eyes 
consciously  focussed  after  any  part  of  the  light  was  seen. 
The  kerosene  lamp  used  was  trimmed  at  the  beginning  of 
the  experiments.  By  photometric  determinations  always 
made  before  a  sitting  and  generally  during  and  after  the 
sitting,  it  was  found  that  the  light  varied  very  little  or  not 
at  all. 

Four  observers  were  tested,  C,  McW.  and  S.  respec- 
tively with  time,  area  and  intensity.  All  were  advanced 
students  in  psychology,  and  S.  had  had  previous  experience 
with  after-images.  F.,  the  writer,  was  the  fourth  observer, 
the  three  series  being  made  upon  him. 

The  results  of  nearly  3,000  experiments  are  given  in  the 
following  tables.  In  the  first  line  the  percentage  of  times 
an  after-image  was  seen  is  given,  and  in  the  second  line  the 
average  variation  of  the  sets  of  ten  trials;  100  experiments 
of  each  sort  were  made,  excepting  in  those  cases  in  which  a 
different  number  is  given  in  parenthesis. 

Some  preliminary  experiments  on  area  made  on  the  writer 
bear  out  in  general  the  results  in  the  corresponding  series. 
These  experiments  were  made  with  an  intensity  of -^^^  c.  p., 
so  that  they  could  not  be  combined  with  the  others.  The 
other  constant  was  an  exposure  of  one  second.  The  same 
areas  w'ere  used  except  that  the  -^^  sq.  mm.  was  omitted. 
Seventy  experiments  were  made  on  each  area.  The  results, 
with  the  average  variations,  are  shown  in  the  accompanying 
table. 


134 


SHEPHERD  IVORY  FRANZ. 
INTENSITY. 


Intensity  in 

candle  power. 

2 
2  5 

1 

200 

¥o3- 

1 

^200 

(  Percentage, 
S. 

(  Variation, 

lOO 

(8o) 

94 

7 
1 

48 

25         (no) 

17 

20.8  (no) 

2 

3-6 

r  Per  cent., 
*    (Var., 

lOO 

96 

5.4 

44 

1 9. 5  (130) 

15-5 
13.5(130) 

I 

1.8 

AREA. 


Area   in 

1 

square  mm. 

64 

16 

4 

I 

¥ 

tV     1 

(  Per  cent.. 

100 

90 

72 

52 

27 

20 

McW.  \ 

(Var., 

—  (50) 

7-5  (80) 

14.8 

12.4 

9.2 

6 

(  Per  cent., 

100 

96 

88 

57 

31 

8 

F-        \ 

I  Var., 

— 

4.8 

8.8 

13 

15-4 

8 

TIME. 


Time  in  seconds. 

I 

1 

1          1           1 

TTT 

lOO         j         1000 

(  Per  cent., 
C. 

(  Var., 

97 

3-5(7°) 

95 

7 

75         :     12 

17              1        10.8 

(  Per  cent., 
(Var., 

100 

97 
4.2 

82.5            19 
8.3(120)          7.4 

THE  AFTER-IMAGE    THRESHOLD. 
AREA. 


135 


Area  in  sq.  mm. 

64   1   16      4       I       \ 

(  Per  cent., 
(Var., 

1       '              ' 
96   1   89     67      41     19 

i              ]       i 
5      10     14.7  j   10      9-9 

The  results  of  the  first  three  tables  are  represented  graph- 
ically by  the  accompanying  curves. 


t'lGURE    2. 


5     1. 

The  abscissa  denotes  respectively  divisions  of  time,  area 
and  intensity,  the  ordinate  the  percentage  of  times  an  after- 
image appeared.  The  curves  are  not  carried  out  to  repre- 
sent the  greatest  intensity,  the  greatest  area  and  the  greatest 
time.  Each  curve  is  the  average  of  the  two  observers  in 
that  series,  the  close  agreement  of  the  observers  making  this 
method  permissible.  The  figures  on  the  abscissa  represent 
the  proportion  of  that  stimulus  to  the  greatest  stimulus, 
taking  respectively  time,  area  and  intensity  as  the  variables. 

If  we  regard  the  threshold  as  that  intensity,  time  or  area, 
which  produces  an  after-image  'j^''/^  of  the  number  of 
stimuli,  we  conclude 

(i).  That  with  an  exposure  of  one  second  and  an  intensity 
of  ^2^  c.  p.,  the  threshold  is  4  sq.  mm. 

(2).  That  with  the  area  64  sq.  mm.  and  the  intensity  -^ 
c.  p.,  the  threshold  is  -^  second. 


I  3  6  SHEPHERD  I VOR  V  ERA  NZ. 

(3).  That  with  the  area  64  sq.  mm.  and  the  time  of  ex- 
posure one  second,  the  threshold  is  y^^  candle 
power  (approximately),  or  between  Jyand  7?,-,,  c.  p. 

If  we  substitute  in  our  definition  25^,  or  50%,  or  90%,  for 
the  75 '^,  we  but  change  the  figures  to  suit  the  case. 

It  is  worth  noting  that  of  the  1,500  cases  when  after- 
images were  seen,  but  five  were  negative,  a  proof  of  the 
theory  that  the  negative  after-image  is  due  to  exhaustion  of 
the  eyes,  the  low  intensities,  the  small  areas  and  the  short 
times  not  being  sufficient  to  tire  or  exhaust  the  eyes.  These 
five  negative  images  were  all  seen  toward  the  close  of  a 
sitting,  when  the  eyes  had  been  used  for  forty  or  fifty  experi- 
ments, and  all  were  with  the  greatest  intensity,  the  longest 
time  and  the  largest  area. 

With  the  results  obtained  we  are  able  to  make  a  further 
comparison — a  correlation  of  our  physical  units  in  terms  of 
the  production  of  after-images — a  purely  psychological  prob- 
lem. How  much  time  equals  how  much  intensity  or  area? 
A  glance  at  the  curves  and  percentages  shows  that  equal 
increments  in  area,  intensity  and  time  do  not  give  equal  re- 
sults. If  Ave  represent  our  constants  by  the  letters  c,  c'  and 
c"  respectively  for  intensity,  time  and  area,  and  let  i,  t  and  a 
represent  respectively  -g^  c.  p.,  xiw^  sec.  and  ^  sq.  mm., 
from  the  table  of  percentages  we  get  the  following  approxi- 
mate equations. — 

i  c  =  t  c'  =  a  c" 
(2  i  c)  —  (1.7  t  c')  =  (4  a  c") 
4  i  c  =  3.2  t  c'  =  16  a  c" 
8  i  c  =  10  t  c'  =  64  a  c" 
16  i  c  =  100  t  c'  =  256  a  Q." 

The  8  i  c  and  the  3.2  t  d  represent  yf^  c.  p.  and  y^  sec. 
(approximately).  These  figures  and  the  second  equation  in 
brackets  are  supplied  from  the  curves.  The  relations,  then, 
may  be  stated  as  follows:  "Squaring  the  time  equals 
doubling  the  intensity  or  quadrupling  the  area,"  and  vice 
versa,  "  reducing  the  area  to  one-fourth  equals  halving  the 
intensity  and  taking  the  square  root  of  the  time."  Whether 
this  be  a  chance  relation  or  a  general  one  throughout  the 
phenomena  of  after-images  cannot  be  dogmatically  stated 
now.    The  writer  has  in  view  the  further  study  of  this  problem. 

1 2  4  9 1  0 


This  book  is  DUE  on  the  last  date  stamped  helow 


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